This paper addresses the description and kinematic analyses of a new non-redundant series-parallel manipulator. The primary feature of the robot is to have a decoupled topology consisting of a lower parallel manipulator, for controlling the orientation of the coupler platform, assembled in series connection with a upper parallel manipulator, for controlling the position of the output platform, capable to provide arbitrary poses to the output platform with respect to the fixed platform. The forward displacement analysis is carried-out in semi-closed form solutions by resorting to simple closure equations. On the other hand; the velocity, acceleration and singularity analyses of the manipulator are approached by means of the theory of screws. Simple and compact expressions are derived here for solving the infinitesimal kinematics by taking advantage of the concept of reciprocal screws. Furthermore, the analysis of the Jacobians of the robot shows that the lower parallel manipulator is practically free of singularities. In order to illustrate the performance of the manipulator, a numerical example which consists of solving the inverse/forward kinematics of the series-parallel manipulator as well as its singular configurations is provided.